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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313876
details
property
value
status
complete
benchmark
quicksortPtime.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.597 seconds
cpu usage
355.386
user time
350.431
system time
4.95463
max virtual memory
3.7974756E7
max residence set size
5406676.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
355.20/291.53 WORST_CASE(Omega(n^1), O(n^2)) 355.20/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 355.20/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 355.20/291.55 355.20/291.55 355.20/291.55 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 355.20/291.55 355.20/291.55 (0) CpxRelTRS 355.20/291.55 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 421 ms] 355.20/291.55 (2) CpxRelTRS 355.20/291.55 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 355.20/291.55 (4) CpxWeightedTrs 355.20/291.55 (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 355.20/291.55 (6) CpxWeightedTrs 355.20/291.55 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 355.20/291.55 (8) CpxTypedWeightedTrs 355.20/291.55 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 355.20/291.55 (10) CpxTypedWeightedCompleteTrs 355.20/291.55 (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 355.20/291.55 (12) CpxTypedWeightedCompleteTrs 355.20/291.55 (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms] 355.20/291.55 (14) CpxRNTS 355.20/291.55 (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 355.20/291.55 (16) CpxRNTS 355.20/291.55 (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 2 ms] 355.20/291.55 (18) CpxRNTS 355.20/291.55 (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 355.20/291.55 (20) CpxRNTS 355.20/291.55 (21) IntTrsBoundProof [UPPER BOUND(ID), 158 ms] 355.20/291.55 (22) CpxRNTS 355.20/291.55 (23) IntTrsBoundProof [UPPER BOUND(ID), 48 ms] 355.20/291.55 (24) CpxRNTS 355.20/291.55 (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 355.20/291.55 (26) CpxRNTS 355.20/291.55 (27) IntTrsBoundProof [UPPER BOUND(ID), 413 ms] 355.20/291.55 (28) CpxRNTS 355.20/291.55 (29) IntTrsBoundProof [UPPER BOUND(ID), 90 ms] 355.20/291.55 (30) CpxRNTS 355.20/291.55 (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 355.20/291.55 (32) CpxRNTS 355.20/291.55 (33) IntTrsBoundProof [UPPER BOUND(ID), 502 ms] 355.20/291.55 (34) CpxRNTS 355.20/291.55 (35) IntTrsBoundProof [UPPER BOUND(ID), 155 ms] 355.20/291.55 (36) CpxRNTS 355.20/291.55 (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 355.20/291.55 (38) CpxRNTS 355.20/291.55 (39) IntTrsBoundProof [UPPER BOUND(ID), 450 ms] 355.20/291.55 (40) CpxRNTS 355.20/291.55 (41) IntTrsBoundProof [UPPER BOUND(ID), 105 ms] 355.20/291.55 (42) CpxRNTS 355.20/291.55 (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 355.20/291.55 (44) CpxRNTS 355.20/291.55 (45) IntTrsBoundProof [UPPER BOUND(ID), 4185 ms] 355.20/291.55 (46) CpxRNTS 355.20/291.55 (47) IntTrsBoundProof [UPPER BOUND(ID), 1640 ms] 355.20/291.55 (48) CpxRNTS 355.20/291.55 (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 355.20/291.55 (50) CpxRNTS 355.20/291.55 (51) IntTrsBoundProof [UPPER BOUND(ID), 713 ms] 355.20/291.55 (52) CpxRNTS 355.20/291.55 (53) IntTrsBoundProof [UPPER BOUND(ID), 266 ms] 355.20/291.55 (54) CpxRNTS 355.20/291.55 (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 355.20/291.55 (56) CpxRNTS 355.20/291.55 (57) IntTrsBoundProof [UPPER BOUND(ID), 189 ms] 355.20/291.55 (58) CpxRNTS 355.20/291.55 (59) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 355.20/291.55 (60) CpxRNTS 355.20/291.55 (61) FinalProof [FINISHED, 0 ms] 355.20/291.55 (62) BOUNDS(1, n^2) 355.20/291.55 (63) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 355.20/291.55 (64) CpxRelTRS 355.20/291.55 (65) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 355.20/291.55 (66) typed CpxTrs 355.20/291.55 (67) OrderProof [LOWER BOUND(ID), 0 ms] 355.20/291.55 (68) typed CpxTrs 355.20/291.55 (69) RewriteLemmaProof [LOWER BOUND(ID), 287 ms] 355.20/291.55 (70) BEST 355.20/291.55 (71) proven lower bound 355.20/291.55 (72) LowerBoundPropagationProof [FINISHED, 0 ms] 355.20/291.55 (73) BOUNDS(n^1, INF) 355.20/291.55 (74) typed CpxTrs 355.20/291.55 (75) RewriteLemmaProof [LOWER BOUND(ID), 61 ms] 355.20/291.55 (76) typed CpxTrs 355.20/291.55 (77) RewriteLemmaProof [LOWER BOUND(ID), 48 ms] 355.20/291.55 (78) typed CpxTrs 355.20/291.55 (79) RewriteLemmaProof [LOWER BOUND(ID), 91 ms] 355.20/291.55 (80) typed CpxTrs 355.20/291.55 355.20/291.55 355.20/291.55 ---------------------------------------- 355.20/291.55 355.20/291.55 (0) 355.20/291.55 Obligation: 355.20/291.55 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). 355.20/291.55 355.20/291.55 355.20/291.55 The TRS R consists of the following rules: 355.20/291.55 355.20/291.55 qs(x', Cons(x, xs)) -> app(Cons(x, Nil), Cons(x', quicksort(xs)))
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